Bayesian Individual Dynamic Predictions with Uncertainty of Longitudinal Biomarkers and Risks of Survival Events in a Joint Modelling Framework: a Comparison Between Stan, Monolix, and NONMEM

Joint modeling of monocyte HLA-DR expression trajectories predicts 28-day mortality in severe SARS-CoV-2 patients

The recent SarsCov2 pandemic has disrupted healthcare system notably impacting intensive care units (ICU). In severe cases, the immune system is dysregulated, associating signs of hyperinflammation and immunosuppression. In the present work, we investigated, using a joint modeling approach, whether the trajectories of cellular immunological parameters were associated with survival of COVID-19 ICU patients. This study is based on the REA-IMMUNO-COVID cohort including 538 COVID-19 patients admitted to ICU between March 2020 and May 2022. Measurements of monocyte HLA-DR expression (mHLA-DR), counts of neutrophils, of total lymphocytes, and of CD4+ and CD8+ subsets were performed five times during the first month after ICU admission. Univariate joint models combining survival at day 28 (D28), hospital discharge and longitudinal analysis of those biomarkers' kinetics with mixed-effects models were performed prior to the building of a multivariate joint model. We showed that a higher mHLA-DR value was associated with a lower risk of death. Predicted mHLA-DR nadir cutoff value that maximized the Youden index was 5414 Ab/C and led to an AUC = 0.70 confidence interval (95%CI) = [0.65; 0.75] regarding association with D28 mortality while dynamic predictions using mHLA-DR kinetics until D7, D12 and D20 showed AUCs of 0.82 [0.77; 0.87], 0.81 [0.75; 0.87] and 0.84 [0.75; 0.93]. Therefore, the final joint model provided adequate discrimination performances at D28 after collection of biomarker samples until D7, which improved as more samples were collected. After severe COVID-19, decreased mHLA-DR expression is associated with a greater risk of death at D28 independently of usual clinical confounders.

Bayesian estimation in NONMEM

Bayesian estimation is a powerful but underutilized tool for answering drug development questions. In this tutorial, the principles of Bayesian model development, assessment, and prior selection will be outlined. An example pharmacokinetic (PK) model will be used to demonstrate the implementation of Bayesian modeling using the nonlinear mixed-effects modeling software NONMEM.

Joint modeling under competing risks: Application to survival prediction in patients admitted in Intensive Care Unit for sepsis with daily Sequential Organ Failure Assessment score assessments

Joint models of longitudinal process and time-to-event data have recently gained attention, notably to provide individualized dynamic predictions. In the presence of competing risks, models published mostly involve cause-specific hazard functions jointly estimated with a linear or generalized linear model. Here we propose to extend the modeling to full parametric joint estimation of a nonlinear mixed-effects model and a subdistribution hazard model. We apply this approach on 6046 patients admitted in intensive care unit (ICU) for sepsis with daily Sequential Organ Failure Assessment (SOFA) score measurements. The joint model is built on a randomly selected training set of two thirds of patients and links the current predicted SOFA measurement to the instantaneous risks of ICU death and discharge from ICU, both adjusted on the patient age. Stochastic Approximation Expectation Maximization algorithm in Monolix is used for estimation. SOFA evolution is significantly associated with both risks: 0.37, 95% confidence interval (CI) = [0.35, 0.39] for the risk of death and -0.38, 95% CI = [-0.39, -0.36] for the risk of discharge. A simulation study, inspired from the real data, shows the good estimation properties of the parameters. We assess on the validation set the added value of modeling the longitudinal SOFA follow-up for the prediction of death compared with a model that includes only SOFA at baseline. Time-dependent receiver operating characteristic area under the curve and Brier scores show that when enough longitudinal individual information is available, joint modeling provides better predictions. The methodology can easily be applied to other clinical applications because of the general form of the model.

A workflow for the joint modeling of longitudinal and event data in the development of therapeutics: Tools, statistical methods, and diagnostics

Clinical trials investigate treatment endpoints that usually include measurements of pharmacodynamic and efficacy biomarkers in early‐phase studies and patient‐reported outcomes as well as event risks or rates in late‐phase studies. In recent years, a systematic trend in clinical trial data analytics and modeling has been observed, where retrospective data are integrated into a quantitative framework to prospectively support analyses of interim data and design of ongoing and future studies of novel therapeutics. Joint modeling is an advanced statistical methodology that allows for the investigation of clinical trial outcomes by quantifying the association between baseline and/or longitudinal biomarkers and event risk. Using an exemplar data set from non‐small cell lung cancer studies, we propose and test a workflow for joint modeling. It allows a modeling scientist to comprehensively explore the data, build survival models, investigate goodness‐of‐fit, and subsequently perform outcome predictions using interim biomarker data from an ongoing study. The workflow illustrates a full process, from data exploration to predictive simulations, for selected multivariate linear and nonlinear mixed‐effects models and software tools in an integrative and exhaustive manner.

Multistate model for pharmacometric analyses of overall survival in HER2-negative breast cancer patients treated with docetaxel

The aim of this study was to develop a multistate model for overall survival (OS) analysis, based on parametric hazard functions and combined with an investigation of predictors derived from a longitudinal tumor size model on the transition hazards. Different states - stable disease, tumor response, progression, second-line treatment, and death following docetaxel treatment initiation (stable state) in patients with HER2-negative breast cancer (n = 183) were used in model building. Past changes in tumor size prospectively predicts the probability of state changes. The hazard of death after progression was lower for subjects who had longer treatment response (i.e., longer time-to-progression). Young age increased the probability of receiving second-line treatment. The developed multistate model adequately described the transitions between different states and jointly the overall event and survival data. The multistate model allows for simultaneous estimation of transition rates along with their tumor model derived metrics. The metrics were evaluated in a prospective manner so not to cause immortal time bias. Investigation of predictors and characterization of the time to develop response, the duration of response, the progression-free survival, and the OS can be performed in a single multistate modeling exercise. This modeling approach can be applied to other cancer types and therapies to provide a better understanding of efficacy of drug and characterizing different states, thereby facilitating early clinical interventions to improve anticancer therapy.

Longitudinal Tumor Size and Neutrophil-to-Lymphocyte Ratio Are Prognostic Biomarkers for Overall Survival in Patients With Advanced Non-Small Cell Lung Cancer Treated With Durvalumab

Therapy optimization remains an important challenge in the treatment of advanced non-small cell lung cancer (NSCLC). We investigated tumor size (sum of the longest diameters (SLD) of target lesions) and neutrophil-to-lymphocyte ratio (NLR) as longitudinal biomarkers for survival prediction. Data sets from 335 patients with NSCLC from study NCT02087423 and 202 patients with NSCLC from study NCT01693562 of durvalumab were used for model qualification and validation, respectively. Nonlinear Bayesian joint models were designed to assess the impact of longitudinal measurements of SLD and NLR on patient subgrouping (by Response Evaluation Criteria in Solid Tumors 1.1 criteria at 3 months after therapy start), long-term survival, and precision of survival predictions. Various validation scenarios were investigated. We determined a more distinct patient subgrouping and a substantial increase in the precision of survival estimates after the incorporation of longitudinal measurements. The highest performance was achieved using a multivariate SLD and NLR model, which enabled predictions of NSCLC clinical outcomes.